Point it out generally without mentioning the person who made the mistake.

Say something like: There are those who say X which implies Y, but of course X can be seen as an error, if you consider the following reasons based on the following assumptions.

Then of course they can come back at your own assumptions and reasoning, which in fact might be wrong.

You must take into account that if they are a prominent scholar they have been raked over the coals many times by many others, and there is a good chance that they have produced all kinds of arguments for their position by which they can defend it. There is a good chance that what you have come up with as a mistake has been brought up to them many times before. Thus the best thing to do is to say something like:

I may be mistaken but what about X which impies Y. And then if you do not get a reasonable answer that has sufficient backing with arguments, then you might want to suggest that they think about their position a bit deeper.

The best way to approach anyone is to say something like. I have similar thoughts that are parallel to yours but diverge in some respect, and I would like to explore the differences and similarities with your thoughts in order to learn more about my own thinking.

Then they will attempt to straighten you out, and you can judge for yourself whether their arguments are sound and persuasive. But the chances of getting them to admit a mistake are slim. However, the greatest minds are those who easily admit mistakes and relish finding the limits of their thought. The greatest minds are not those with the deepest thoughts or the most profound thoughts but which never change their mind and defend their positions to the death. The greatest minds are those who are poised for an opportunity to grow and learn and sieze that opportunity as soon as it appears. Of course, they will defend their positions until they are sure that what ever is suggested is genuinely better than their own thoughts on the subject, but once they discover that someone else has thought deeper than they have about the subject and are correct in their reasoning, then they embrace the change and move on to explore the new territory that is opened up for them by the constructive criticism of others.

As socrates said the greatest of us are those who know they don’t know, not those who think that they do know. Socrates discovered he was wisest because he knew he did not know the answers to everything. But in this journey of abandoning position after position where knowledge seemed secure but was discovered to be limited in some respect one develops wisdom, and that wisdom is really the most precious thing we can attempt to possess ourselves.